The Tory arts spokesman, Ed Vaizey, was strolling home one night before the election when he was suddenly met by a gang of hoodies. They dragged him into an alley, slammed his head against a wall and told him never, ever to reintroduce museum charges. They then broke his fingers and said he should "tell that George Osborne he gets the same". They knew where his children lived.

A petrified Vaizey stammered out a promise that he and Osborne would treat "free entry as iconic". So they did. They had just had their first encounter with London's arts mafia. But appeasing the powerful seldom yields peace of mind. Another gang, the Treasury, was already furious at the coalition ringfencing the NHS, overseas aid and the Olympics. This was another case of weak ministers being mugged by a metropolitan lobby – and someone would have to pay.

Meanwhile lurking behind the muggers was London's mayor, Boris Johnson. He champions free museum entry and a general exemption from all cuts, since the capital has a "special status as an engine for growth … Its economy is bigger than those of Scotland, Northern Ireland, Wales and the East Midlands combined". He wants a ringfence round the entire capital, woven of taxpayer gold. To any provincials who complain of unfairness, the mayor says of London's largesse, "any diminishing of it will be to the detriment of the entire country". As goes London, so goes the nation. Trickle-down is alive and living in City Hall.

In recent months Johnson has fiercely defended the high-cost, £9bn version of the Olympics. He has defended the £12bn Crossrail project in addition to a multibillion-pound tube upgrade programme. He called any threat to Crossrail "madness", any cut in housing subsidy "insane", and any cut in police numbers "barking". He has demanded no taxes for non-doms and no super-taxes for bankers. Last week he opened two new cycle lanes that succeeded in costing £43m.

The mayor is filling London streets with electronic bays for an exotic cycle-sharing scheme. He is blowing £50m by shrinking the congestion charge zone. He has rescued the senseless London Development Agency. He has refused to cut back on the 2012 games, even salvaging the unfundable Olympic Village. He is bidding both for the football World Cup and a new airport in the Thames estuary. He is the wildest of old-style big spenders.

There is no doubt London will take a hit from reductions in public spending, directed principally at bureaucratic overheads. The assault on quangos and on such extravagances as management consultants, privatisation lawyers, advertisers, conferences and hospitality will hurt the capital.

But the experience of past recessions is that London is resilient. It has already done well from the weak pound and from staycationing, with theatres and entertainment showing record takings in 2009. Financial services are far from down and out, surging to pre-crash levels of activity and profit. Commercial property is healthy, and London house prices have regained their former buoyancy. Plutocratic flats are rising over Knightsbridge and along the south bank of the Thames. Almost every road in the capital is being expensively reconstructed. London has money to burn, and is burning it.

The transport secretary, Philip Hammond, probably spoke for the rest of the nation when he remarked recently that, "there is a feeling, justified or unjustified, that London gets a very good deal" from taxpayers. When he added that "public money is better spent on maintenance of existing infrastructure than on new projects", he was sending a clear signal that the game is up.

As a lifelong Londoner I am acutely aware of the good fortune with which my home town is blessed. As a provincial traveller, I am equally aware how provincial cities have squandered money on urban renewal that has merely desecrated their centres and weakened their identity and vitality. Britain would still benefit from an architectural "truth and reconciliation commission" to atone for the civic horrors of the 1970s and 1980s.

But London's good fortune does not qualify it for special treatment. The proclaimed engine of its prosperity, banking, was overwhelmingly the cause of the collapse in public finances. It was also the overwhelming beneficiary of the subsequent state handout. Why should these bankers get their galleries for nothing, and their theatre and opera subsidised at the expense of the rest of the nation? Why should the Tate in London be free when Cornish yokels must pay £5.75 to visit the Tate St Ives?

The London behemoths on which Johnson wants millions spent – tubes, airports, museums, sports stadiums – are beyond the dreams of provincial Britain. That they are "iconic" merely means that powerful middle-class lobbies are behind them. It is an open secret that Transport for London strategists have long been sceptical of Crossrail. When he left in April 2009, TfL's then boss, Tim O'Toole, pleaded with colleagues to concentrate on upgrading the tube, fearing that London would end the next decade with years of Crossrail chaos still ahead, while the rest of the undercapitalised network degenerated. Johnson was half-persuaded of this, until the construction industry lobby told him Crossrail was a virility symbol and he capitulated. Hammond should kill the project forthwith.

Johnson's spendthrift approach to public expenditure is because in 2012, he will probably face a challenge from Ken Livingstone. This Rip Van Winkle of British politics is already gaily campaigning on his old platform of opposing "Tory cuts". Johnson is desperate to avoid being tarred with that Thatcherite brush.

There is a straightforward way out of this bind. It was put forward by LSE's Tony Travers and myself in these pages last year. London now raises just 7% of its local needs from its own taxes, against 50% in New York and 80% in Tokyo. It should be empowered to raise its own revenue. This cause has been taken up by Johnson's own policy director, Anthony Browne, who this month pointed out that "London is the most fiscally infantilised big city on earth". While it yields gargantuan revenue to the state, its own taxation, based on static property bands, has no buoyancy.

Browne rightly argues that the mayor should be pleading not with the government but with his own electors for cash. He cannot be excused from central government cuts, but he should be free to raise compensating resources from London's taxpayers. That is the route open to most mayors abroad.

The best scheme would be the one floated by Sir Kenneth Calman for the Scottish parliament. It would cut London's gross income tax by, say, 10% in year one, and cut grants to London from central government by an equivalent amount. It would then be left to Johnson and borough leaders to make up the 10% from whatever mix of local income tax, council tax or business rates they chose. If they wanted to go over 10% from local income tax to pay for Crossrail or whatever, so be it.

Londoners – indeed residents anywhere – should be entitled to relief from the pain now afflicting the nation. They should not expect others to pay for it. They should be able to pay for it themselves.

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